Bounds on Diatomic Molecules in a Relativistic Model

TL;DR

This paper establishes bounds on the number of electrons, binding energy, and bond distance for diatomic molecules using a relativistic kinetic energy model, advancing understanding of molecular stability in relativistic quantum mechanics.

Contribution

It introduces bounds on molecular parameters within a relativistic framework, utilizing localization techniques and Scott correction analysis, which are novel in this context.

Findings

Bounds on the maximum number of electrons for stability

Quantitative estimates of binding energy

Predictions of equilibrium bond distance

Abstract

We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of electrons, the binding energy $\Delta E_b$ and the equilibrium bond distance $R_0$. We use a known localization argument adopted to the present relativistic setting, with particular consideration of the critical point of stability, as well as the recently proved relativistic Scott correction.